How to proceed with research after finding you aren't who you thought you were

I have been researching my Avery ancestors for the past 40 years. Everyone who researches this bunch gets back to Jacob Avery b. ca 1784 and gets stuck. So I decided to do DNA testing to see if I could break this road block and find some more people working on the family.  I tested out to 67 markers and find that I am more closely related to the Perry family than to the Avery family. One of the Perrys matches 66 of 67 markers. No Averys in sight. How do I interpret this result and how do I proceed in researching them? Thanks for your help